1. Field of the Invention
This invention relates to a driving apparatus for driving a driven member such as an XY stage in a measuring machine.
2. Description of the Prior Art
A joy stick having an operating lever capable of being inclined in any direction can put out electrical signals corresponding to an X direction component and a Y direction component corresponding to the direction of inclination of the operating lever from a neutral position. When the hand is released from the operating lever, the operating lever returns to the neutral position.
In an XY stage of a three-layer structure a Y direction driving apparatus may comprise for example, a motor and a Y direction lead screw provided on a reference member, and a Y direction stage provided for sliding movement on the reference member only in Y direction and having a frame threadably engaged with the Y direction lead screw. An X direction driving apparatus similar to the Y direction driving apparatus is provided on the Y direction stage, and the frame of an X direction stage is provided on the Y direction stage for sliding movement only in X direction and is threadably engaged with the X direction lead screw of the X direction driving apparatus. The motor of the X direction driving apparatus and the motor of the Y direction driving apparatus can be designed so as to be driven by electrical signals corresponding to the X direction component and the Y direction component which are obtained from the joy stick.
Apparatuses designed such that the control of the movement of the XY stage is accomplished by the operating lever of the joy stick in this manner are already commercially available.
In an apparatus of this type, in order to execute a wide range of velocity commands, as shown in FIG. 1 of the accompanying drawings, there is provided a joy stick designed such that the division ratio of an X direction potentiometer 2a and a Y direction potentiometer 2b for dividing a reference voltage correspondingly to the direction of inclination and the angle of inclination of an operating lever 1a varies. A accordingly electrical signals indicative of the X direction component and the Y direction component which are put out from the respective potentiometers 2a and 2b (the former is an X signal Vx and the latter is a Y signal Vy) vary. The X signal Vx and the Y signal Vy are input to nonlinear transforming circuits 3a and 3b, respectively, and the output signals of the nonlinear transforming circuits 3a and 3b pass through motor driving circuits 4a and 4b and are applied to an X direction motor 6a and a Y direction motor 6b for moving an XY stage 5 in X and Y directions.
In such a conventional apparatus, however, the X signal Vx and the Y signal Vy have been non-linearly transformed directly correspondingly to the X and Y directions of the stage, and this has led to the following disadvantages:
(1) Generally, the angle of inclination of the joy stick from the neutral position of the operating lever and the velocity of movement of the stage do not primarily correspond to each other, and the velocity of movement of the stage depends on the direction of inclination of the joy stick in the xy coordinates system; and
(2) Generally, the direction of inclination of the operating lever of the joy stick (which corresponds to the azimuth angle or the declination in the polar coordinates) and the direction of movement of the stage do not coincide with each other.
This will hereinafter be described in detail with respect to a two-dimensional example.
If the angles of inclination of the operating lever in X and Y directions are .theta.x and .theta.y, there is the following relation between the X signal (voltage) Vx from the potentiometer 2a and the Y signal Vy from the potentiometer 2b: EQU Vx=a.theta.x, Vy=a.theta.y (1)
where a is a suitable constant.
Here, let it be assumed that in a three-dimensional rectangular coordinates system comprising x, y and z axes, when the operating lever is in its neutral position, the operating lever is coincident with the z axis and the center of inclination of the joy stick is coincident with the origin of the coordinates. Then, .theta.x is the angle formed between the image of the operating lever projected onto the xz plane and the z axis, and .theta.y is the angle formed between the image of the operating lever projected onto the yz plane and the z axis.
Also, when the angle of inclination of the joy stick is displayed in polar coordinates and use is made of the absolute value .vertline..theta..vertline. of the angle of inclination and the azimuth angle .phi., .theta.x and .theta.y are expressed by tan .theta.x=tan .theta..multidot.cos .phi. and tan .theta.y=tan .theta..multidot.sin .phi., but when .theta. is small, .theta.x and .theta.y are approximately expressed as follows: EQU .theta.x.noteq..vertline..theta..vertline. cos .phi., .theta.y.noteq..vertline..theta..vertline. sin .phi. (2)
If it is assumed that a cubic function is used as an example of the nonlinear characteristic, outputs V'x and V'y nonlinearly transformed with the voltage outputs Vx and Vy being received are expressed by the use of a constant p, ##EQU1##
The motor driving circuits 4a and 4b receive these voltages V'x and V'y and effect control so that the stage is moved at velocities proportional thereto. That is, if it is assumed that by the use of a suitable constant q, the velocities v.sub.x and v.sub.y of the stage in x and y directions are given by ##EQU2## then the movement velocity components v.sub.x and v.sub.y of the stage are displayed in polar coordinates with the absolute value .vertline.v.vertline. of the velocity and the direction of movement .phi.v being expressed as follows: ##EQU3##
Further, if the direction of movement .phi.v of the stage is differentiated by the direction of inclination .phi. of the operating lever, there is obtained: ##EQU4##
From equation (5), it is seen that the movement velocity .vertline.v.vertline. of the stage not only primarily corresponds only to the angle of inclination .vertline..theta..vertline. of the operating lever but also corresponds to .phi. in the radical sign, i.e., the direction of inclination of the operating lever. This is shown in FIG. 2 of the accompanying drawings. It is seen that, as shown in FIG. 2, .vertline.v.vertline. should be constant irrespective of the value of the direction of inclination .phi., but actually a maximum double fluctuation occurs with a variation in .phi..
Also, from equation (6), it is seen that the direction of movement .phi.v of the stage should ideally coincide with the direction of inclination .phi. of the operating lever, but actually the two do not coincide with each other. This is shown in FIG. 3 of the accompanying drawings. It is only when the angle of inclination is 0.degree., 45.degree., 90.degree., . . . that the two coincide with each other, and when 0.degree..ltoreq..phi.&lt;45.degree., the direction of movement of the stage is transformed to the 0.degree. side, and when 45.degree.&lt;.phi..ltoreq.90.degree., the direction of movement of the stage is transformed to the side approximate to 90.degree.. Therefore, when the direction of movement of the stage is to be controlled by the joy stick, the operating lever must not be inclined in a direction coincident with a desired direction of movement, but must be inclined in a direction usually approximate to 45.degree.. Equation (7) is one in which this direction of movement of the stage is differentiated by the direction of inclination of the operating lever and, as shown in FIG. 4 of the accompanying drawings, the differential coefficient should ideally be fixed to 1, but actually it exhibits a fluctuation O in the vicinity of the direction of inclination of 0.degree. or 90.degree. and exhibits a great fluction 3 in the vicinity of the direction of inclination of 45.degree.. That is, even if the direction of inclination of the operating lever is delicately changed in the vicinity of the direction of inclination of 0.degree. or 90.degree., the direction of movement of the stage will hardly change, and if conversely the operating lever is inclined in the vicinity of the direction of 45.degree., a slight deviation of the direction will greatly affect the direction of movement.
From the foregoing consideration, it is apparent that sufficient accuracy of operation cannot be obtained in the nonlinear transforming system as shown in FIG. 1 and the operator is forced to bear an inordinate burden. In the foregoing consideration, a cubic function has been used as the nonlinear function, but it will be readily understood that a qualitatively similar characteristic is exhibited even when use is made of a different nonlinear function.